arXiv subjects
Publications and source records attributed to M. Yu. Trofimov.
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method.
A pure analytic one-way coupled mode propagation model for resonant interacting modes is obtained by the multiscale expansion method. It is proved that the acoustic energy flux is conserved in this model up to the first degree of the corresponding small parameter. The test calculations with the COUPLE program give an excellent agreement.
A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for ASA wedge benchmark and proved excellent agreement with COUPLE program.
A forced, variable coefficients Kor\-te\-weg-de Vries equation for amplitudes of long, nonlinear internal waves in a stratified shear flow over topography is derived when the magnitude of the basic flow is small. The derivation is done by incorporating the basic flow in the perturbation series of the Taniuti and Wei's reductive perturbation method. Istead of the long-wave Tailor-Goldstein spectral problem, only the usual long-wave spectral problem for rested stratified media and a boundary value problem have to be solved for calculating the coefficients of obtained equation. Explicit expressions for these coefficients are presented.
Ray mode parabolic equations which are suitable for shallow water acoustics propagation problems are derived by the multiple-scale method.
An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.
The narrow and wide-angle parabolic equations for the quasi-monochromatic sound wave packets propagating in a waveguide with a non-stationary background flow are obtained. The results of numerical simulations are presented.
The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary condition at low computational cost.
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation.
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.